Question

The expression \((6 + 5\sqrt{3}) - (4 - 3\sqrt{3})\) is:

• A. Rational number
• B. Irrational number
• C. Natural number
• D. None of the above

Hint:

When dealing with expressions involving square roots, if the result involves an irrational number like \(\sqrt{3}\), the entire expression is typically irrational.

Answer 1

The Correct Option is B

Simplifying the expression: \[ (6 + 5\sqrt{3}) - (4 - 3\sqrt{3}) = (6 - 4) + (5\sqrt{3} + 3\sqrt{3}) = 2 + 8\sqrt{3} \] Since \(\sqrt{3}\) is an irrational number, multiplying it by 8 still results in an irrational number. Hence, the result is an irrational number.